Find Sum to infinity of the given series: a. 1 + 2x + 3x² + 4x³+... to ∞ (|x| <1)
​

Answer:

To divide two mixed numbers, we need to first convert them to improper fractions.

10 1/4 is the same as (10 x 4 + 1)/4 = 41/4

5 1/2 is the same as (5 x 2 + 1)/2 = 11/2

So, we need to divide 41/4 by 11/2:

(41/4) ÷ (11/2)

When dividing by a fraction, we can multiply by its reciprocal (flip the fraction):

(41/4) x (2/11)

Now, we can simplify by canceling out the common factors:

(41 x 2) / (4 x 11) = 82/44 = 41/22

Therefore, 10 1/4 divided by 5 1/2 is equal to 41/22 or approximately 1.86 when rounded to two decimal places.

Por lo tanto, 10 1/4 dividido por 5 1/2 es igual a 41/22 o aproximadamente 1,86 cuando se redondea a dos decimales.

There is a 2.28% likelihood that the average weight of the bags in a randomly selected pack is 2 or more grams lighter than advertised.

Assume that the advertised weight is equivalent to the typical weight of one bag, which is 30 grammes. A pack of nine bags would therefore weigh 9 x 30 = 270 grammes.

Let's now assume that each bag actually weighs 30 grammes on average, with a 2 gramme standard deviation, according to a normal distribution (which represents the variability in the weight of the bags).

We need to apply the central limit theorem to determine the probability that the average weight of the bags in a randomly selected pack is 2 or more grammes less than stated. According to this theorem, the mean of a sufficiently large sample (in this case, nine bags) will have a sampling distribution that is roughly normal, with a mean of 30 grammes and a standard deviation of 2 grammes divided by the square root of the sample size (9 = 0.67 grammes). The mean will also be equal to the population's standard deviation.

We can determine the likelihood that the sample mean of a pack of 9 bags weighs less than 28 grammes using a normal distribution table or calculator (which is 2 grammes less than the advertised weight of 30 grams). This likelihood is roughly 0.0228, or 2.28%.

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The quantity of paper that needed to wrap 6 mini muffins is 84.857 inches^2

The surface area of a cylinder can be calculated using the formula:

Surface Area = 2πr^2 + 2πrh

where r is the radius of the cylinder (which is half of the diameter) and h is the height of the cylinder.

For the mini muffins in question, the diameter is 2 inches, so the radius is 1 inch. The height is 1 and 1/4 inches, or 5/4 inches.

So the surface area of one mini muffin is:

Surface Area = 2π(1)^2 + 2π(1)(5/4)

Surface Area = 2π + 5π/2

Surface Area = 9π/2

To wrap 6 mini muffins, we need to multiply this surface area by 6:

Total Surface Area = 6 x (9π/2)

Total Surface Area = 27π

Approximating π as 22/7, we get:

Total Surface Area ≈ 27 x (22/7)

Total Surface Area ≈ 84.857 inches^2

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Answer:

The quantity of paper that needed to wrap 6 mini muffins is 84.857 inches^2

Step-by-step explanation:

I don't know but i can help a little

Step-by-step explanation:

But If the slops are the same and the y-intercepts are different, the lines are parallel...

No, we cannot conclude that 90% of households have between .7 and 2.1 children based on the confidence interval alone.

Based on the confidence interval alone, we cannot come to the conclusion that 90% of households have a number of children between .7 and 2.1. A confidence interval only provides a range of values that likely contains the true population parameter (in this case, the average number of children per household) with a certain level of confidence (in this case, 90%). It does not provide information about the distribution of the variable within the population. Therefore, we cannot make any conclusions about what percentage of households have a certain number of children based on the confidence interval alone.

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So, the system of equations solution is (x, y) = (-27/8, 31/4), and the value of y in this solution is 31/4, which is roughly 7.75. As a result, the answer is y = 31/4.

An equation is a statement in mathematics that states the equality of two expressions. An equation has two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine which variable(s) must be changed in order for the equation to be true. Simple or complex equations, regular or nonlinear equations, and equations with one or more elements are all possible. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are employed in a variety of mathematical disciplines, including algebra, calculus, and geometry.

the system of equations,

[tex]y = 1 - 2x\\2x - 3(1 - 2x) = -30\\2x - 3 + 6x = -30\\8x = -27\\x = -27/8\\2(-27/8) + y = 1\\-27/4 + y = 1\\y = 1 + 27/4\\y = 31/4[/tex]

So, the system of equations solution is (x, y) = (-27/8, 31/4), and the value of y in this solution is 31/4, which is roughly 7.75.

As a result, the answer is y = 31/4.

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37.5% of the area between 550 and 725 on a standardized test of educational achievement lies within one standard deviation of the mean score of 600.

The area between 550 and 725 on a standardized test of educational achievement is equal to the percentage of students whose scores fall within one standard deviation (or 68%) of the mean score of 600. This can be expressed mathematically as:

Percentage = (725 - 550) / (2 * 50) = 37.5 / 100 = 37.5%

To explain in more detail, a standard deviation is a measure of the spread of a dataset around its mean value. The mean value in this case is 600, and the standard deviation is 50. Therefore, one standard deviation from the mean is calculated by subtracting or adding the standard deviation (50) from the mean (600), giving a range of 550 to 650.

Since the area in question spans across two standard deviations (550 to 725), the area is calculated by subtracting the lower range (550) from the upper range (725) and then dividing it by two standard deviations (100). This gives us the area, which is 37.5%.

To summarize, 37.5% of the area between 550 and 725 on a standardized test of educational achievement lies within one standard deviation of the mean score of 600.

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25 gallons of water will be dumped on Mr. Henderson's head.

To solve the problem, we first need to find the total amount of water dumped on Mr. Henderson's head by all the students. Since each student dumps a 5-quart bucket of water, we can find the total amount by multiplying the number of students by the amount of water per student:

Total amount of water = 20 students x 5 quarts/student = 100 quarts

Next, we convert the total amount of water from quarts to gallons since the problem asks for the answer in gallons. Since 1 gallon equals 4 quarts, we can divide the total amount of water by 4 to get the answer in gallons:

Total amount of water = 100 quarts ÷ 4 quarts/gallon = 25 gallons.

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The magazine would cost $33.93 to print a 1¾ inch ad in the "Good Ole Times" magazine.

The cost of a classified ad in the "Good Ole Times" magazine is determined by its size in column inches, with a cost of $43.50 per column inch. To determine how much the magazine would charge to print a 1¾ inch ad, we need to calculate the size of ad in column inches and then multiply that by the cost per column inch.

One way to convert 1¾ inches to column inches is to convert the fractional part (¾) to a decimal by dividing it by 4, which is the number of quarters in an inch. This gives us:

1¾ inches = 1 + ¾ inches = 1 + 0.75 inches = 1.75 inches

To express this measurement in column inches, we divide by the width of a column, which is not given in the problem. Assuming a typical newspaper column width of 2.25 inches, we get:

1.75 inches ÷ 2.25 inches per column = 0.7778 column inches

Rounding this to two decimal places, we get:

0.78 column inches

Now we can calculate the cost of the ad as follows:

Cost = Size in column inches × Cost per column inch

Cost = 0.78 column inches × $43.50 per column inch

Cost = $33.93

Therefore, the magazine would charge $33.93 to print a 1¾ inch ad.

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Answer:

I attached your answer along with an explanation

Step-by-step explanation:

Please Like me follow me and Give me Crown for more help. :)

Honestly I think you need some theray feom reading your tabs

Answer:

6.6

Step-by-step explanation:

The formula for a paralellogram is base x height (not side length). the base in this case is 2.2 and the height is 3, so 2.2 x 3 = 6.6.

Let me know if this helped you by hitting thanks or brainliest. If not, please comment and I will get back to you ASAP!

Using the scale factor of 4:1, the side lengths of the real objects are:

B. Side a is 5 inches long and side b is 4.5 inches long.

A scale factor is a number that represents the ratio of the size or dimensions of an object in relation to another object. It is a proportional relationship between two similar objects, where the scale factor is the ratio of any corresponding lengths or dimensions.

Thus, given that the scale factor is 4:1, it means 4 inches of the scale drawing represents 1 inch of the real object.

Therefore, the sides would be:

Side a = 20/4 = 5 in.

Side b = 18/4 = 4.5 in

The answer is B.

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Answer:

The answer to our problem is, $17.75

Step-by-step explanation:

First we need to find out what is 25% of 71

25% of 71 is 17.75. Or [tex]17\frac{3}{4}[/tex] We would need to stick to the term in decimals because of we are using money. Have you ever heard of a fraction in money my guess is no. So let’s stay with decimals. 17.75

How I got it:

25 percent * 71

= (25:100)* 71

= (25* 71):100

= 1775:100

= 17.75

Percentage solution with steps:

71 = 100% (1)

X = 25% (2)

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of bothequations have the same unit (%); we have

[tex]\frac{71}{x} = \frac{25}{100}[/tex]

X = 17.75

Thus the answer to your problem is, $17.75

The exponential function that relates the total population, is [tex]P(t)=540,000\left [ 1+(5.1/100) \right ]^t[/tex] and the rate at which the population is increasing in the year 2019 is 69114.53.

The exponential function in mathematics is represented by the symbol eˣ (where the argument x is written as an exponent). The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, however it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

we know that ,

the population of any city can be modeled in the form of exponential function as follows:

[tex]P(t)=P(0)(1+R)^t[/tex]    

where, P(t)=population of the town at any given time t

P(0)=population of the town initially (in the year 2000 for this problem)=540,000

R=rate of increase (=5.1% in the given problem)

substituting the values in eqn(1), we get

[tex]P(t)=540,000\left [ 1+(5.1/100) \right ]^t[/tex]

as we know that

[tex]\because \frac{d}{dx}(a^x )=a^xln(a)[/tex]

so differentiating w.r.t. we get,

[tex]P'(t)=540,000\left [ 1+(5.1/100) \right ]^t*ln(1+(5.1/100) )\\\\P'(t)=540,000\left [ (105.1/100) \right ]^t*ln(105.1/100)\\\\P'(t)=540,000\left [ (1.051) \right ]^t*ln(1.051)[/tex]

so, the rate at which population is increasing in the year 2019 =

[tex]P'(19)=540,000(1.051)^{19}*ln(1.051)[/tex]

P'(19)= 69114.53.

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Complete question:

The population of Toledo, Ohio, in the year 2000 was approximately 540,000. Assume the population is increasing at a rate of 5.1 % per year.

a. Write the exponential function that relates the total population, P(t), as a function of t, the number of years since 2000. P(t) = =

b. Use part a. to determine the rate at which the population is increasing in t years. Use exact expressions. P'(t) people per year

c. Use part b. to determine the rate at which the population is increasing in the year 2019. Round to the nearest person per year. P'(19) = people per year

Step-by-step explanation:

Please give brainliest

1a) 3√49

3 x √49

3x 7 =21

b) 2³√64

2 x √4

2x2 =4

c) (√x+2)²

the square will cancel the square root

= x+2

Answer:

These are correct

Step-by-step explanation:

1. a) 21

1. b) 8

1. c) x+2

2. a) x/10 and subtracting or simplifying it gives you the same answer

2. b) 2(3x-1)/ x+3 the operation is simplifying

2. c) 7x+2/ x(x+1) combine the fractions and find a common denominator

2. d) 6/x simplify

2. e) 2x^2 simplify or divide

3. a) 6x^3 y^4

3. b) 16a^2 b^6

3. c) 4x^2

3. d) 2

It sounds like you may be experiencing a bug with your Alexa device. This is likely due to a software update or miscommunication between the device and the server.

To resolve this issue, you may need to restart your device by unplugging it from the power source and plugging it back in. You can also try clearing the cache of your device. Additionally, you may need to update the software of your device by visiting the Amazon website and downloading the most recent version of the software. If the issue persists, you may need to contact Amazon customer service for further assistance.

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As per the given percentage, the total number of beings surveyed is 75.

We are given that 96% of all beings on earth prefer orange juice. This means that if we take a random sample of beings from earth, 96% of them would prefer orange juice. Mathematically, we can express this as:

Percentage of beings who prefer orange juice = 96%

We are also given that 72 people preferred orange juice. We can use this information to find the total number of beings surveyed. Let's assume that the total number of beings surveyed is "x".

Now, we know that 96% of these beings prefer orange juice. We can express this as:

96% of x = 72

To solve for "x", we need to get rid of the percentage sign. We can do this by converting the percentage to a decimal. To convert a percentage to a decimal, we divide it by 100.

So, 96% can be expressed as 0.96 (96/100). Therefore, we can rewrite the above equation as:

0.96x = 72

To solve for "x", we can divide both sides of the equation by 0.96:

x = 72 ÷ 0.96

x = 75

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Answer:

20$

Step-by-step explanation:

since there is a discount we first find the discount allowed which is 40$. After we also use the coupon which is 50% off. then you get 20$ as your answer

Yet because we can compare the set of positive rational numbers exactly to the collection of natural numerals, we may infer that the set of positive rational must have a number of clusters of 0, or n(Q+)=0. Due to the fact that these two numbers must equal one another, 02 = 0.

Since they may be arranged in a one-to-one correspondence with the natural numbers (the integers, such as 1, 2, and 3), Cantor showed in 1873 that the rational numbers, although being infinite, are countable (or denumerable).

How are the rational numbers counted as a group?

To achieve this, we take into account the this double integers grid upon that positive orthogonal. If p and q are positive natural numbers, then p/q may be used to represent any positive valid value.

Simply put, we establish the following values: h(0) = 0, h(2n) = f(n), for all natural numbers n > 0, and h(2n-1) = g(n) = -f(n), for all natural numbers n > 0.

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A graph of the image of ABC under a dilation whose center is P and scale factor is 1/3 is shown in the image below.

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric shape, but not its shape. This ultimately implies that, the size of the geometric shape would be increased (enlarged) or decreased (reduced) based on the scale factor applied.

In this exercise, we would use an online graphing calculator to plot the image of ABC after a dilation by a scale factor of 1/3 centered at P.

Based on the image (see attachment), we can logically deduce that each vertex is 1/3 times as far from center P as the original vertex and each segment is 1/3 times as long as the original:

Side length AC = 6.7/3 = 2.2

Side length AB = 12.4/3 = 4.1

Side length CB = 12.7/3 = 4.2

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Complete Question:

Draw the image of triangle △ABC under a dilation whose center is P and scale factor is 1/3.

The only option that represetns a function is the linear equation:

y = 4x - 19

A function is a relation that maps elements from one set, the domain, into elements of another set, the range.

Such that a relation is only a function if each element of the domain is mapped into a single value from the range.

For example, if you look at the second option, here we have the relation:

(-15, 10).(-15, 5),(-10, 0).(-10,-5).(-5, -10)

You can see that the input x = -15 is mapped into two different values, y = 10 and y = 5, so this is not a function.

In the other hand, the first option:

y = 4x - 19

Is a function, this is a linear equation, and each value of x gives a different value of y.

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Answer:

Complementary angles: a pair of angles are considered complementary when their sum is exactly 90º.

Step-by-step explanation:

To calculate a complementary angle, we will subtract 90 from the angle that the statement tells us and it will give us its complementary. Supplementary angles: A pair of angles are considered supplementary when their sum is exactly 180º.

We can claim that after answering the above question, the Therefore, the solution to the original equation is: [tex]q = 9^x\\[/tex]

In mathematics, an equation is a statement that states the equality of two expressions. An equation consists of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" states that the sentence "2x Plus 3" equals the value "9". The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.

given equation:

[tex]1/4xln(16q^8) - ln3 = ln24\\1/4xln(16q^8) = ln(24 * 3)\\1/4xln(16q^8) = ln72\\ln(16q^8)^(1/4x) = ln72\\16q^8^(1/4x) = 72\\16q^8 = 72^(4x)\\ln(16q^8) = ln(72^(4x))\\[/tex]

[tex]ln(16) + ln(q^8) = 4x ln(72)\\ln(q^8) = 4x ln(72) - ln(16)\\ln(q^8) = ln(72^(4x)) - ln(16^1)\\ln(q^8) = ln((72^(4x))/16)\\q^8 = e^(ln((72^(4x))/16))\\q^8 = (72^(4x))/16\\q^8 = 9^(8x)\\q = 9^x\\[/tex]

Therefore, the solution to the original equation is:

[tex]q = 9^x\\[/tex]

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Here are some examples:

Distance to endpoint: |2 - (-2)| = 4

Equation: |x - 2| = 4



When answering questions on Brainly, you should always be factually accurate, professional, and friendly. You should be concise and not provide extraneous amounts of detail. You should also use the following terms in your answer, if they are relevant to the question being asked.

In order to write an absolute value equation in the form |x-c|=d to satisfy a given solution set on a number line, you need to do the following:First, identify the number c, which is the midpoint of the solution set. This is because the absolute value of x-c is equal to the distance between x and c on the number line.

Next, identify the number d, which is equal to the distance between the midpoint c and one of the endpoints of the solution set. This is because the absolute value of x-c can never be greater than the distance between x and c, so the maximum value of x that satisfies the equation is c+d and the minimum value is c-d.Finally, write the equation in the form |x-c|=d using the values of c and d that you identified.

Set of solutions (-3, 1) In the middle: (-3 + 1)/2 = -1

Endpoint distance: |-1 - (-3)| = 2

Formula: |x + 1| = 2

Set of solutions (-4, 4)

Center: (-4 + 4)/2 = 0.

Endpoint distance: |0 - (-4)| = 4

Equation: 4 for |x| Set of solutions (-2, 6)

Center: (-2 + 6)/2 = 2

Endpoint distance: |2 - (-2)| = 4

Equation: 4 for |x - 2|

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Bending moment curve equation below point A will be:

M = 15x - 3x² for 0 ≤ x ≤ b

Determination of shear and bending moment curves.

For the beam and loading shown, we can do the following:

Equation of shear curve (above point A):V = RA - w.x

For x = a,V = RA - w.a

For x = b,V = RA - w.b

Since the loading is symmetric, RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15 - 6a for a ≤ x ≤ b

Equation of shear curve (below point A):

V = RA - w.x

For x = 0,V = RA - w.0RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15k for 0 ≤ x ≤ a

The shear curve equation becomes;

V = 15k for 0 ≤ x ≤ a

V = 15 - 6a for a ≤ x ≤ b

Equation of bending moment curve (above point A):

M = RAx - ½w.x²For 0 ≤ x ≤ a,

M = 15x - ½(6x²) = 15x - 3x²For a ≤ x ≤ b,

M = 15x - 6a(x - a) - ½(6x²)= 15x - 6ax + 6a² - 3x²

The bending moment curve equation above point A becomes:

M = 15x - 3x² for 0 ≤ x ≤ a

M = 15x - 6ax + 6a² - 3x² for a ≤ x ≤ b

Equation of bending moment curve (below point A):

M = RAx - ½w.x²For 0 ≤ x ≤ b,

M = 15x - ½(6x²) = 15x - 3x²

The bending moment curve equation below point A becomes;

M = 15x - 3x² for 0 ≤ x ≤ b

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The Area of the given quadrilateral or four sided polygon is equal to the value of 36 cm².

Given,

Length of the Rectangle is equal to 6 cm.

Breadth of rectangle is 4 cm.

Height of the right angled triangle is 4 cm.

Length of the base of the triangle is 3 cm.

First we need to find the area of single then multiply it with 2 since the lengths of the triangles are same and the area will also be same.

⇒ Area of Triangle = [tex]\frac{1}{2} * b *h[/tex]

Area of Triangle = [tex]\frac{1}{2}[/tex] * 4 * 3

Area of Triangle = 6 cm².

Now, area of two triangles is equal to 2 * 6 cm² = 12 cm².

⇒ Area of Rectangle = length * breadth

Area of Rectangle = 6 * 4

Area of Rectangle = 24 cm²

Now, total area = Area of Triangle + Area of Rectangle

Total area = 12 cm² + 24 cm²

Total area = 36 cm².

Therefore, the Area of the given quadrilateral or four sided polygon is equal to the value of 36 cm².

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Answer: 36

Step-by-step explanation:

4(9/3)(2) = 36

Answer:

x(z ÷ 3)² = 36

Step-by-step explanation:

Given expression,

→ x(z ÷ 3)²

Now we have to use,

→ x = 4

→ z = 9

Let's simplify the expression,

→ x(z ÷ 3)²

→ 4(9 ÷ 3)²

→ 4 × (3)²

→ 4 × 9

→ 36 => {answer}

Therefore, the answer is 36.

The above table represents the contents ( colored marble) of a bag. The probability that selected marble had a color other than white or blue is equals to the 0.766234 ( nearest to milinoth).

We have a bag that contains five different types of marbles. See the above table

number of red marbles in a bag = 16

number of green marbles in a bag = 23

number of blue marbles in a bag = 13

number of pink marbles in a bag = 20

number of white marbles in a bag = 5

So, total number of marbles in a bag= 16 + 23 + 5 + 13 + 20 = 77

Now, a single marble is selected and out of the bag. We have to determine probability that it is a color other than white or blue. Let X , Y and Z be three events defined as the following

X = selected marble is white

Y = selected marble is blue

Z = selected marble is other than blue or white

Probability of seclecting white marble, P(X) = 5/77

Probability of seclecting blue marble, P(Y)

= 13/77

Probability of seclecting blue or white marble, P(Y UX) = P(X) + P(Y) = 5/77 + 13/77 = 18/77

So, probability that selected marble has a color other than white or blue, P(Z) = 1 - P( X UY) = 1 - 18/77

= 59/77 = 0.76623376623

Hence, required probability is 0.766234.

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Complete question :

The above table discribes the contents of a bag that contains red,green, blue,pink and white marbles if you select a single marble out of the bag, what is the probability that it is a color other than white or blue? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.